As far as I experienced there are three ways to create a vibrato. First is to change mechanically between blowing harder and softer which works quite good for a slow and intense vibrato. If you play around a while with increasing and reducing tempo, you may find out that there is a certain tempo where it feels like you don’t have to do anything to keep up a vibrato. That’s because your diaphragm takes over and beginns to move up and down automatically. (That’s the vibrato most singers use as it is a vibrato that doesn’t influence your larynx, so the vocal cords can swing freely.) It’s also called the natural vibrato because you don’t have to do anything to “produce” it; so you don’t have to move your belly in and out, it works by itself! Only thing is, you can’t influence the tempo of that vibrato, it just remains constant. And the third way is what you described, to use your throat, which is especcially useful for very quick vibratos. The faster you go and the more you actually close your throat, the more it sounds goat-like, which might be useful to imitate a swing clarinet. (But it’s not the real thing because that would require a tremolo – I tried to produce a tremolo by bending fast but it’s nearly impossible!)
With these three ways you should be able to produce a vibrato just as fast and intense as you want.